Numerical Calibration of Stress Intensity Factor for Transversely Isotropic Central Cracked Brazilian Disk

To obtain the stress intensity factors (SIFs) of transversely isotropic central cracked Brazilian disk (CCBD), an anisotropy coefficient f is introduced based on the isotropic analytical formula. The coefficient f is related to the anisotropy orientation beta, the anisotropy ratio of Young's modulus xi, and the apparent shear modulus eta. The comprehensive calibration of f is accomplished by the finite element method. Then the formulae for mode I and II SIFs are obtained by fitting f to the analytical solutions of the isotropic CCBD, which realizes the generalization and application of the formulae in transversely isotropic rocks based on the isotropic condition. The new formulae presented in this paper can calculate the SIFs for any given elastic modulus, crack length, anisotropy orientation and certain loading angle range (0 degrees-25 degrees). The results show that the relative errors between the formula and the numerical simulation results are within 5%, and the relative errors with other researches are within 2.8%. Both the SIFs and the correlation coefficients M-1(beta), M-2(beta), and N-1(beta) show a variation of sine or cosine concerning the anisotropy orientation beta. And the influence of xi and eta on SIFs can be negligible by adjusting beta to some specific angles given in this paper.